For the most part, big and large mean the same thing. The only difference you will find is when using these words more creatively. For example, we might say, "Jimmy is a big man on campus." This means Jimmy is very popular on campus. We wouldn't customarily say, " Jimmy is a large man on campus."

Either can be used to mean the same thing. If you wanted to say something is VERY big you could choose a word that denotes that such as Enormous or Huge. For example 'The house was large but the castle was enormous'.

Sometimes they mean the same thing. Other times, it is a matter of custom or idiom . You can say to a child " You're a big boy now" meaning grown up; you're a large boy is not used but would refer to physical size. The room was big / large means the same thing. You would have a big idea, but not a large idea. By and large is an idiom meaning "in general". By and big would make no sense! There isn't a simple black and white answer...